Sum-Product Networks: A New Deep Architecture

TL;DR

Sum-Product Networks (SPNs) are a novel deep architecture enabling efficient inference in graphical models, combining tractability with expressive power, and outperforming traditional deep networks in tasks like image completion.

Contribution

Introduction of sum-product networks (SPNs), a new deep architecture with tractable inference, and development of learning algorithms demonstrating superior performance.

Findings

SPNs can efficiently compute marginals and partition functions.

SPNs outperform standard deep networks in image completion tasks.

SPNs are more general than many existing graphical models.

Abstract

The key limiting factor in graphical model inference and learning is the complexity of the partition function. We thus ask the question: what are general conditions under which the partition function is tractable? The answer leads to a new kind of deep architecture, which we call sum-product networks (SPNs). SPNs are directed acyclic graphs with variables as leaves, sums and products as internal nodes, and weighted edges. We show that if an SPN is complete and consistent it represents the partition function and all marginals of some graphical model, and give semantics to its nodes. Essentially all tractable graphical models can be cast as SPNs, but SPNs are also strictly more general. We then propose learning algorithms for SPNs, based on backpropagation and EM. Experiments show that inference and learning with SPNs can be both faster and more accurate than with standard deep networks. For example, SPNs perform image completion better than state-of-the-art deep networks for this task. SPNs also have intriguing potential connections to the architecture of the cortex.